Answer:
a.i [tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii. time at which vat will be empty
[tex]T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex] when dQ/dt = 0
b. i Amount of salt at time t
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
ii. Concentration at t = T
c(T) = [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Step-by-step explanation:
a.
i. We determine the differential equation for the solution in the vat at time,t.
Let Q be the quantity of salt in the vat at any time,t.
So, dQ/dt = rate of change of quantity of salt in the vat. = rate of change of quantity of salt into the vat - rate of change of quantity of salt out of the vat.
Now, since a concentration of salt, k enter the vat at a rate of rin, rate of change of quantity of salt into the vat = krin.
Let V(0) = V₀ be the volume of water int the vat at time t = 0. Now, the volume of water in the vat increases at a rate of (rin - rout). The increase in volume after a time t is (rin - rout)t. So the volume after a time, t is V(t) = V₀ + (rin - rout)t. The concentration of this liquid is thus Q(t)/V(t) = Q(t)/V₀ + (rin - rout)t. Now, the rate of change of quantity of salt out of the vat is thus [Q(t)/V₀ + (rin - rout)t]rin = Q(t)rout/[V₀ + (rin - rout)t].
So, dQ(t)/dt = krin - Q(t)rout/[V₀ + (rin - rout)t].
[tex]\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[/tex]
ii Time T at which vat will be empty
At time T, when the vat is empty, dQ(T)/dt = 0.
So
[tex]\\\frac{dQ(T)}{dt} + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\0 + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}[/tex]
b. i
i. We solve the differential equation to find the amount of salt at time,t
The integrating factor is ex
[tex]exp(\int\limits {\frac{r_{out} }{V_{0} + (r_{in} - r_{out})t} } \, dt ) = exp(\frac{r_{out}}{(r_{in} - r_{out})} \int\limits {\frac{ (r_{in} - r_{out})}{V_{0} + (r_{in} - r_{out})t} } \, dt )\\= exp(\frac{r_{out}}{(r_{in} - r_{out})} ln [V_{0} + (r_{in} - r_{out})t} ]) \\\= [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]
Multiplying both side of the equation by the integrating factor, we have
[tex][V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{dQ(t)}{dt} + [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})[/tex]dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt = krin[V(0) + (rin - rout)texp(rout/(rin - rout))]
Integrating both sides we have
∫(dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt)dt = ∫(krin[V(0) + (rin - rout)texp(rout/(rin - rout))])dt
Let exp(rout/(rin - rout) = A
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + C
At t = 0, Q(t) = Q(0),
So,
Q(0)[V(0) + A(rin - rout)×0] = AkrinV(0)t + A(rin - rout)×0²/2 + C
C = Q(0)V(0)
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + Q(0)V(0)
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
The above is the amount of salt at time ,t.
ii. The concentration of the last drop of salt at time, t = T
To find the concentration of the last drop of salt at time t = T, we insert T into Q(t) to find its quantity and insert t = T into V(t) = V₀ + (rin - rout)t.
So
Q(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]
Q(T) = [[exp(rout/(rin - rout)]krin[V(0)T + [exp(rout/(rin - rout)](rin - rout)T²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)T]
the volume at t = T is
V(T) = V₀ + (rin - rout)T.
The concentration at t = T is c(T) = Q(T)/V(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]/V₀ + (rin - rout)T.
= [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/([V(0) + A(rin - rout)T][V₀ + (rin - rout)T])
= [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Find the Coordinates of a point A, where AB is diameter of a circle whose
centre is (2,-3) and B is (1,4)
Answer:
(3, -10)
Step-by-step explanation:
let A(x,y) and B(x1,y1)=(1,4)
by midpoint formula i.e. (x+x1)/2 ; (y+y1)/2
as midpoint is centre so,
(2, -3) = (x+1)/2 ; (y+4)/2
2=(x+1)/2 and -3=(y+4)/2
4-1=x and -6-4=y
x=3 and y=-10
therefore A(x,y)=A(3,-10)
Asphere has a radius of 4 in. Which equation finds the volume of the sphere?
Answer:
[tex]V = \frac{4}{3} \pi r^{2}[/tex] - is the formula for the volume of a circle.
Step-by-step explanation:
Step 1:
- Insert your values:
- [tex]V = \frac{4}{3} \pi 4^{2}[/tex]
Step 2:
- Simplify using order of operations:
- Exponents First:
- [tex]V = \frac{4}{3} \pi 64[/tex]
- Division Second:
- [tex]V = 1.333 \pi 64[/tex]
- Multiplication Last:
- [tex]V = 268.01555[/tex]
- And Simplified:
- V = 268 (approx.)
Hope this helps! Good luck!
At a costumer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. What is the probability that during a given hour of the day there will be between 146 calls and 163 calls, to the nearest thousandth
We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.
First of all, we will use z-score formula to find z-score corresponding to 146 and 163.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{146-150}{5}[/tex]
[tex]z=\frac{-4}{5}[/tex]
[tex]z=-0.8[/tex]
[tex]z=\frac{163-150}{5}[/tex]
[tex]z=\frac{13}{5}[/tex]
[tex]z=2.6[/tex]
Our next step is to find percentage of data scores falls between both z-scores.
[tex]P(-0.8<z<2.6)=P(z<2.6)-P(z<-0.8)[/tex]
Using normal distribution table, we will get:
[tex]P(-0.8<z<2.6)=0.99534-0.21186[/tex]
[tex]P(-0.8<z<2.6)=0.78348[/tex]
Let us convert our answer into percentage.
[tex]0.78348\times 100\%=78.348\%[/tex]
Upon rounding our answer to nearest thousandths, we will get:
[tex]78.348\%\approx 78.35\%[/tex]
Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately [tex]78.35\%[/tex].
Answer:
0.624
Step-by-step explanation:
DeltaMath
Help! I just don't understand
Answer:
$71
Step-by-step explanation:
Since x denotes the number of miles and we know that the car rode 100 miles, this means that x=100, and when we plug this in, we get C(x) = 0.5* 100 + 21 = 50 + 21 = $71. Hope this helps!
Answer:
C(100) = 71
Step-by-step explanation:
C(x) = .5x+21
Let x= 100
C(100) = .5(100)+21
= 50+21
= 71
At a local baseball game, the concession stand has two different meal choices. You can get 5 hotdogs and 4 drinks for $15.50 or you can get 6 hotdogs and 3 drinks for $15.00. If the price of hotdogs and drinks is the same for each meal, find how much it costs for an individual hotdog and an individual drink.
per hordog =
per drink=
Answer: Hot Dog $1.50 Drinks $2.00
Step-by-step explanation:
What is the distance between A(-8, 4) and B(4, -1)?
Answer:
10.908
Step-by-step explanation:
20% of US High School teens vape. A local High School has implemented campaigns to reduce vaping among students and believes that the percentage of students who vape at this High School is lower than the national average. School administration implements a survey of 300 randomly selected students. They find that 51 of the 300 vape.
If the true proportion of students who vape at this school is 20%, what is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Answer:
10.93% probability of observing 51 or fewer vapers in a random sample of 300
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 300, p = 0.2[/tex]
So
[tex]\mu = E(X) = np = 300*0.2 = 60[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.2*0.8} = 6.9282[/tex]
What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Using continuity corrections, this is [tex]P(X \leq 51 + 0.5) = P(X \leq 51.5)[/tex], which is the pvalue of Z when X = 51.5 So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{51.5 - 60}{6.9282}[/tex]
[tex]Z = -1.23[/tex]
[tex]Z = -1.23[/tex] has a pvalue of 0.1093.
10.93% probability of observing 51 or fewer vapers in a random sample of 300
What is value of 3x2+4y2if x=2, y=1, and z=-3
Answer:
16
Step-by-step explanation:
3x² + 4y² where x = 2, y = 1, and z = -3
Here we just need to plug in the given values to their respective variables
3(2)² + 4(1)² There are no z variables in this equation so plugging in z = -3 is irrelevant Simplifying our equation we now have: 3(4) + 4(1) = 12 + 4 = 16Answer:
0 if the original expression is : 3x^2 + 4yz
Step-by-step explanation:
3x^2 + 4yz ; I guess this is the original expression.
When x=2, y = 1 z =-3
3x^2 + 4yz = 3(2)^2 + 4 × (1)×(-3)
= 3×4 + 4 × (-3) = 12 - 12 = 0
if a is a positive number then -a^6 is
Where do you find your domain restrictions in a rational function?
Answer:
denominator zeros are excluded
Step-by-step explanation:
The domain is the set of values of the independent variable where the function is defined. A rational function is "undefined" where the denominator is zero.
The exclusions of interest are generally those values of the variable that make any denominator be zero.
__
Example:
f(x) = (2/(x-3)) / (4/(x -6))
has denominators of x-3 and x-6. These are zero for x=3 and x=6, so those two values are excluded from the domain of this function. We observe that the function can be simplified to ...
f(x) = (x -6)/(2(x -3))
but x=6 remains excluded from the domain because of its effect in the original function definition.
_____
Additional comment
If the rational function includes functions that have domain restrictions (such as square root, for example), then those restrictions apply as well.
Usually, but not always, the rational functions where you're asked about domain are the ratios of polynomials. So, you need to factor or otherwise find the zeros of any denominator polynomials in such functions.
A file that is 278 megabytes is being downloaded. If the download is 19.9% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
55.3
Step-by-step explanation:
19.9% of 278 = 55.322
55.322 rounded to the nearest tenth = 55.3
Answer:55.3
Step-by-step explanation:
what is the product of 72 x 0.45
Answer:
32.4
Step-by-step explanation:
Answer:
32.4
Step-by-step explanation:
Product means the answer of a multiplication problem. So 75 x 0.45 = 32.4.
[tex]75 \times 0.45 = 32.4[/tex]
Hope this helped :)
What is the surface area of the triangular prism?
Triangular prism
a
252 square feet
b
264 square feet
c
152 square feet
d
172 square feet
Answer:
a) 252 square feet
Surface area of triangular prism = 252 square feet
Step-by-step explanation:
Explanation:-
Given diagram Base = 3 feet
Height of the triangular = 4 feet
The slant height of triangular prism 'l' =20 feet
The hypotenuse of the triangle 'c' = 5 feet
prism base area 'p' = h+b+c = = 4 +3+5 =12
Surface area of triangular prism
= [tex]2 (\frac{1}{2} )bh +lA[/tex]
= b h + p l
= 3 ×4 + 12×20
= 252 square feet
Final answer:-
Surface area of triangular prism = 252 square feet
Answer:
252
Step-by-step explanation:
The main span of bridge A is 2500 is percent shorter than the main span of bridge B 4100
Answer:
16%
percentage is calculated by 100
A. 2500 × 1/100 = 25%
B. 4100 x 1/100 = 41%
41% - 25%
16%
therefore bridge A is 16% shorter than bridge B
Please answer this correctly
Answer:
40 cm.
Step-by-step explanation:
So what I tried to do in this case is compare 96 to 64. I subtracted those two numbers which is 32. So since thats the difference between those two shapes, I did the same thing with 72 and I subtracted it but 32, which led me to 40.
Hope this helped :)
Answer:
u=48
Step-by-step explanation:
In similar triangles, corresponding sides have the same ratio.
64/96=u/72
Step 1: Cross-multiply
(64)*(72)=u*(96)
4608=96u
Step 2: Flip the equation.
96u=4608
Step 3: Divide both sides by 96.
96u /96=4608 /96
u=48
Here is a Fill in the Gaps Question:
A prism is a three-______________ shape with the same _______________ all the way through.
Please help.
Jake :)
P.S you will get 40 pts :)
Answer:
A prism is a three-dimensional shape with the same cross-section all the way through.
Step-by-step explanation: Im not sure if i got the second right
A prism is a three-dimensional shape with the same cross-section all the way through.
A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.
What is called prism?A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve.
To learn more about prism, refer
https://brainly.com/question/24071123
#SPJ2
help due timed !! help plss
Answer:
290 m
Step-by-step explanation:
3*6*5=90
5*5*8= 200
200+90=290
Jamie says the value of 1.43 × (− 22 43 ) is close to −0.75. Student A says this estimate is reasonable because the product is negative and about half of 1.5. Student B says you could find the product using a calculator as follows: "Divide −22 by 43, multiply the quotient by 1.43, then round the product to the nearest hundredth." Does student B's approach to find the product justify the claim that Jamie's estimate is reasonable?
Answer:
Student A says this estimate is reasonable because… Get ... Student A says this estimate is reasonable because the product is negative and about half of 1.5. Student B says you could find the product using a calculator as follows: "Divide −18 by 35, multiply the quotient by 1.43, then round the product
Step-by-step explanation:
calculations with a calculator or computer we need a way of checking that the answers it ... introduce students to this way of thinking and give them practice at estimating simple ... Do they always get the right answer no matter what? Invent a story illustrating a calculator error that you may have made or use the following.
Two swimmers at opposite ends of a ninety-foot pool start to swim the length of the pool, one at 3 feet per second and the other at 2 feet per second. If they swim back and forth for twelve minutes, how many times do they pass each other?
Answer:
20 times
Step-by-step explanation:
The faster swimmer can swim twice the length of the pool in ...
(2·90 ft)/(3 ft/s) = 60 s
The slower swimmer can do it in ...
(2·90 ft)/(2 ft/s) = 90 s
The least common multiple of these times is 180 s = 3 minutes, after which time each swimmer will be back where they started.
A graph of position vs. time shows the swimmers pass 5 times in that 3-minute period. 4 of those are passes when they are going in opposite directions. A 5th pass occurs at one end of the pool, when the faster swimmer passes the slower one going in the same direction.
Since there are 5 passes in each 3-minute period, there are 20 passes in 12 minutes.
The swimmers pass each other 20 times in 12 minutes.
An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
What is the probability that all of the sprinklers will operate correctly in a fire?
Answer:
2.82% probability that all of the sprinklers will operate correctly in a fire
Step-by-step explanation:
For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The probability of a sprinkler operating correctly is independent of other sprinklers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.
This means that [tex]p = 0.7[/tex]
10 sprinklers.
This means that [tex]n = 10[/tex]
What is the probability that all of the sprinklers will operate correctly in a fire?
This is P(X = 10).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]
2.82% probability that all of the sprinklers will operate correctly in a fire
The probability that all sprinklers will operate correctly in a fire is 0.028
How to determine the probabilityThe given parameters are:
p = 0.7 ---- the probability that a sprinkler to activate correctly
n = 10 --- the number of sprinklers
The probability that all sprinklers activate correctly is calculated as:
[tex]P(10) = p^n[/tex]
So, we have:
[tex]P(10) = 0.7^{10[/tex]
Evaluate
[tex]P(10) = 0.028[/tex]
Hence, the probability that all sprinklers will operate correctly in a fire is 0.028
Read more about probability at:
https://brainly.com/question/25870256
your choices are
Right
Obtuse
Acute
Answer:
obtuseacuteStep-by-step explanation:
Think about a right triangle with legs AB and AC. Then you have ...
AB² +AC² = BC² = 10² = 100
If AB and AC are shorter than that, the sum of their squares will be less than 100. When the legs of a right triangle are shortened, the angle between them must increase in order for them to continue to form a triangle.
The triangle with AB² +AC² < 100 is an obtuse triangle.
__
Conversely, if AB and AC are lengthened so the sum of their squares is greater than 100, the angle between them will have to decrease for them to form a triangle.
The triangle with AB² +AC² > 100 is an acute triangle.
Recently, More Money 4U offered an annuity that pays 6.3% compounded monthly. If $1,986 is deposited into this annuity every month, how much is in the account after 8 years? How much of this is interest?
Answer:
[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
[tex] I = 3283.153 -1986 = 1297.153[/tex]
Step-by-step explanation:
For this case we can use the formula for the future value using compound interest given by:
[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]
Where P= 1986 the initial amount invested. r = 0.063 represent the interest rate. n=12 represent the number of times that the rate is compounded in a year. And t =8 years . Replacing the info we got:
[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]
So then after 8 years we will have in the account 3283.153
And in order to find the interest we can do the following operation:
[tex] I = 3283.153 -1986 = 1297.153[/tex]
Please help with this
Three less than one-fourth of product of eight thirds and nine, write the expression
Answer:
1/4(8/3+9)-3
Step-by-step explanation:
1/4(8/3+9)-3
I need help with B ASAP because work is due tomorrow and Im seriously stuck. I have tried so many, please help.
Part A is correct; good job.
The universe is even numbers between 1 and 25, that's 2 thru 24. Count; there are twelve of them.
There's only one of them in the intersection of A and B, namely 8.
So the probability is one in twelve.
Answer: 1/12
Type the correct answer in each box.
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is _ units. The point (-15,_) lies on this circle.
Answer:
17, 23
Step-by-step explanation:
First, to find the radius, we need to find the distance between the center of the circle, (-7, -1), and the point that the circle passes through, (8, 7). Plugging these coordinates into the distance formula we do [tex]\sqrt{(-7-8)^2+(-1-7)^2}[/tex] which gives us 17. Therefore, the radius of the circle is 17 units.
Next to find the y-coordinate of the point (-15, ), we need to write out the equation of the circle and then plug in the point. The equation of the circle would be [tex](x+7)^{2} +(y-8)^{2}=289[/tex]. Now we can plug in -15 for x and solve for y. So now we have [tex](-15+7)^{2} +(y-8)^{2}=289[/tex].
Simplifying the equation we have [tex](8)^{2} +(y-8)^{2}=289[/tex]. Subract [tex]8^{2}[/tex] from 289 and now the equation is [tex](y-8)^{2}=225[/tex]. Square root both sides to get [tex]y-8=15[/tex]. We solve for y to get 23. Therefore, the point is (-15, 23).
Answer:
Well, the answer would be 17,23 Also i had the same question as you so i already know the answer
A standard fair dice is rolled twice.
What is the probability of getting an odd number on the first roll and any factor of 12 on the other?
Answer:
5/12
Step-by-step explanation:
The probability of rolling an odd number is 3/6, which is 1/2
The probability of rolling a factor of 12 is 5/6 (1,2,3,4,6)
1/2 x 5/6 = 5/12
It’s about angles use an equation to solve and ABCD?
And what is the measure of RST?
Answer:
A. 40 degree+ 90 degree = x
The sum of the angles = 130 degree
Step-by-step explanation:
[tex]Given:\:\:\angle RSV = 40\degree,\:\:\angle VST = 90\degree\\\because \angle RSV + \angle VST = \angle RST\\\therefore 40\degree + 90\degree = x[/tex]
x = 130 degree
which expression is equivalent p^6)2
So the right answer is p^12.
Look at the attached picture
Hope it will help you
Good luck on your assignment..
Answer:
[tex] {p}^{12} [/tex]
Step-by-step explanation:
[tex]( {p}^{6} ) ^{2} [/tex]
[tex]p ^{6 \times 2} [/tex]
[tex] {p}^{12} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
In the past, the mean running time for a certain type of flashlight battery has been 8.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result.
The hypotheses are:
H0: μ = 8.6 hours
Ha: μ > 8.6 hours
where μ is the mean running time of the new batteries.
Explain the meaning of a Type II error.A. The manufacturer will decide the mean battery life is greater than 8.3 hours when in fact it is greater than 8.3 hours. B. The manufacturer will decide the mean battery life is less than 8.3 hours when in fact it is greater than 8.3 hours. C. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is 8.3 hours. D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours. E. The manufacturer will decide the mean battery life is greater than 8.3 hours when in fact it is 8.3 hours.
Answer:
H0: μ = 8.3 hours
Ha: μ > 8.3 hours
We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:
D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.
Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified
Step-by-step explanation:
For this case we want to determine if mean running time has increased as a result of the new change so then the system of hypothesis are given by:
Note: we assume that the value to check in order to be consistent with the options is 8.3
H0: μ = 8.3 hours
Ha: μ > 8.3 hours
We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:
D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.
Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified